Foetron Interview Questions, Process, and Tips

East

C. Every real number is a rational number.

Can someone confirm that it is : 5/9 * 4/8 * 3/7 = 11.9% that you choose 3 good bulbs in a row

114

grand daughter

63:45:55

let (xy) be original number.
then, 10y + x +45 = 10x + y; eq 1
and x + y = 13; eq 2
solve ab equation,
then xy = 94;

b

1728

Relative velocity of trains = 49kmph -25 kmph = 24kmph
=6.67m/s
Time taken to cross the first train = 10 sec
Length of the second train = Relative Velocity * Time taken
to cross the first Train = 6.67 *10 = 66.7 metres

192 zeros in 1 to 1000

To determine how many consecutive zeros the product of S will end with, we need to find the highest power of 10 that divides the product. This is equivalent to finding the highest power of 5 that divides the product, since the number of factors of 2 will always be greater than the number of factors of 5.

The primes in S are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.

There are 24 primes in S, so the product of S is:

2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97

We need to find the highest power of 5 that divides this product. To do this, we count the number of factors of 5 in the prime factorization of each number in S.

5 appears once: 5
5 appears once: 25
5 appears once: 35
5 appears once: 55
5 appears once: 65
5 appears once: 85
So, there are six factors of 5 in the product of S. However, we also need to consider the powers of 5 that arise from the factors 25, 35, 55, and 65.

25 = 5 x 5 appears once: 25
35 = 5 x 7 appears once: 35
55 = 5 x 11 appears once: 55
65 = 5 x 13 appears once: 65
Each of these numbers contributes an additional factor of 5 to the product of S. Therefore, there are 6 + 4 = 10 factors of 5 in the product of S.

Since each factor of 5 corresponds to a factor of 10, we know that the product of S will end with 10 zeros. Therefore, the product of S will end with 10 consecutive zeros

1208.9

91

( d ) Cannot be determined

yes

30